CRITERION FOR THE NUMBER OF EMPLOYEES IN THE NETWORK FOR PROJECT IMPLEMENTATION WITHOUT DOWNTIME JOBS
UDC 519.86
Key words: network chart, critical path, full path, parallel works, network planning task, project duration, sufficient number of employees.
For citation: Busnyuk N. N. Criterion for the number of employees in the network for project implementation without downtime jobs. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 1 (242), pp. 61–64 (In Russian). DOI: https://doi.org/10.52065/2520-2669-2021-242-2-61-64.
Abstract
In the classical problem of network planning the project duration is equal to the critical path length in the corresponding graph network. The critical paths can be different for the same graph, depending on the values of the arcs weights. In practice this corresponds to the fact that employees with different labor productivity can work on the same projects. The project duration (the length of the critical path) will depend on the way as employees are placed on the corresponding jobs.
Jobs lying on the same path can only be performed sequentially; therefore, one employee is necessary and sufficient for their implementation. Jobs that do not lie on the same path can be performed simultaneously, provided that there are employees not employed in other jobs. The possibility of starting the next job depends on how quickly the previous job is completed. It is important for the project manager to know how many employees must be available at each moment of time in order to: firstly, the jobs do not stand idle and the critical path does not lengthen; and secondly, so as not to keep in reserve employees who are not needed.
The article proves a theorem about how many employees are necessary and sufficient for any project, depending on the structure of the corresponding graph-network, to be carried out without downtime.
References
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